Where \({U}^{(i)}=\text{Toep}(u_0^{(i)},\hdots , u_{T-1}^{(i)})\)  and \(y^{(i)}=[y_{0}^{(i)} \ y_{1}^{(i)} \ \ldots \ y_{T-1}^{(i)}] \in \mathbb {R}^{p \times T}\) . Note that there are different methods from Eq REF  to formulate the least square problem, depending on how the input/output data samples are collected and utilized [1]}, [2]}. All the existing work [3]}, [1]}, [5]}, [6]}, [7]}, [2]} shows that the estimated Markov parameters converge to the true Markov parameters at a rate of \(O(\frac{1}{\sqrt{N}})\) , where \(N\)  is the number of trajectories, regardless of the algorithm used.
